British Rail has been designing active suspensions for some 16 years, starting with tilt systems for the Advanced Passenger train. These have been designed using classical control techniques requiring a combination of experience, intuition and frequency response stability techniques, such as Nichols' plots. In order to see if a more systematic approach to control system design could produce improvements in performance and implementation the current investigation was instigated in which controllers designed using classical techniques are compared with controllers designed using linear optimal control theory. The active suspension used for the investigation was an Electro Magnetic active vertical suspension fitted to a service MkIII coach. Design of the actuators is described in the thesis along with the design of analogue and digital control systems. Two classical control systems were designed. a simple "Sky Hook" damper control system and a more sophisticated position control system developed from British Rail's experience with Maglev suspensions. A regulator designed using linear optimal control theory was found to give very good results in theory. However to implement the regulator it was necessary to design a system observer. In order to achieve a practically realisable observer considerable rationalisation of the vehicle model was required, which drew heavily on experience gained designing classical control systems. The classical control systems proved to be much easier to commission than the optimal controllers as they were designed with implementation in mind. During track testing problems of interaction between vehicles were encountered, as a result the biggest improvements in ride were obtained with the simple Sky Hook damper, as it was less specific to the vehicle than the other configurations. With further development one of the optimal control systems considered will probably turn out to be the most effective as it draws on the attributes of both classical and optimal design techniques.

Three decades have passed since milestone publications by several industrial and academic researchers spawned a flurry of research and commercial, industrial activities on model predictive control (MPC). The improvement in efficiency of the on-line optimization part of MPC led to its adoption in mechanical and mechatronic systems from process control and petrochemical applications. However, the massive strides made by the academic community in guaranteeing stability through state-space MPC have not always been directly applicable in an industrial setting. This thesis is concerned with design and a posteriori certification of feasibility/stability of input-output MPC controllers for industrial applications without terminal conditions (i.e. terminal penalty, terminal constraint, terminal control). MPC controllers which differ in their modelling and prediction method are categorized into three major groups, and a general equivalence between these forms is established. Then an overview on robust set invariance is given as it plays a fundamental role in our analysis of the constrained control systems. These tools are used to give new tuning guidelines as well as a posteriori tests for guaranteeing feasibility of the suboptimal or optimal predictive control law without terminal conditions, which is fundamental towards stability of the closed loop. Next, penalty adaptation is used as a systematic procedure to derive asymptotic stability without any terminal conditions and without using set invariance or Lyapunov arguments. This analysis however is restricted to repetitive systems with input constraints. Then, predictive control without terminal conditions is considered for nonlinear and distributed systems. The invariance tools are extended to switching nonlinear systems, a proof of convergence is given for the iterative nonlinear MPC (NMPC), and a guarantee on overall cost decrease is developed for distributed NMPC, all without terminal conditions. Reference generation and parameter adaptation are shown to be effective mechanisms for NMPC and distributed NMPC (DNMPC) under changing environmental conditions. This is demonstrated on two benchmark test-cases i.e. the wet-clutch and hydrostatic drivetrain, respectively. Terminal conditions in essence are difficult to compute, may compromise performance and are not used in the industry. The main contribution of the thesis is a systematic development and analysis of MPC without terminal conditions for linear, nonlinear and distributed systems.

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